For truly longitudinal continents I would expect that the currents would continue to flow around as with the Antarctic circumpolar current. Depending on how large the continents are in vertical extent then I might expect to see something like what happens on the northern side of the Indian Ocean.

http://www.eeb.ucla.edu/test/faculty...eanography.htm and http://www.sonoma.edu/users/f/freide...lec2images.htm are reasonably good introductions to the subject of physical oceanography if you're having problems in that area.

I don't know of a good physically-based oceanic/atmospheric heat transport model, unfortunately.